Material Instances Using Same Node Set Up
It's true that making duplicate material, the new material is a new entity. But what you may miss is since you have multiple materials in an object, the object may still use the same material as the sphere. Try this:


Select the object with multiple materials.
Enter edit mode, select faces that you want (or I assume you want to select everything)
The materials section now will have Assign, Select, and Deselect.
While the faces are selected, select the material you want from the materials list, then press Assign button.



  I click on the Icon NEW MATERIAL (indicated in Teal colour), so I can
  duplicate the existing material Node set up and assign it on another
  object(s).


You don't have to do this to be able to assign it for another object. You can just select other object, then click the material icon next to the name field, then choose the previous material with the node set up. 
Note that Blender doesn't save unused material (indicated by 0 in front of the material name when you click materials list), means the next time you open the file, they won't be there, so instead you can just make sure the material is used by an object to not disappear later when you open your file.
OR you can also preserve unused material by clicking the shield icon (fake user button) next to the duplicate button, so it is saved even though no object is actually using it.